(5)IhWm132F2(x,x2) 当且仅当:任意a∈D,Iba3n2FP(x1,2) 当且仅当:任意a∈D,存在b∈D,使得 I o(aia(] F(x1, 22) 当且仅当:任意a∈D,存在b∈D,使得:<a,b>∈R 最后一个条件是成立的,因为只要取b=a即可 故Ih132F 例3.22 C与11如例320,σ为C在1中的任一个指派.问在I1中是否 满足下面的公式B vx1Vx2(x3P2(f3(x1,x23),x2)Ax4F2(f3(x2,x4),x1)→F2(x1,x2) 答:1B 对任意m1∈N (x1/1) (3x3F2(3(x1,x3),x2) ∧彐x4F2(f3(x2,x4),x1)→F2(x1,x2) 对任意的m1∈N,m∈N, (x1/1 m72 (彐x3F2(3(x,x3),x2)x4F2(3(x2,x4),x1)→F2(x1,x2 对任意m1,m2∈N 若11 T(x1/m1)(x2/m2 彐x3F2(f(x1,x3),x2)∧彐x4F2(3(x2,x4),x1), 则I1 0(x1/m1)(x2/m2)(5) I | σ ∀x1∃x2F2 (x1, x2) FMNF:/ a ∈ D, I | σ(x1/a) ∃x2F2(x1, x2). FMNF:/ a ∈ D, Y b ∈ D, Z[ I | σ(x1/a)(x2/b) F2(x1, x2). FMNF:/ a ∈ D, Y b ∈ D, Z[ < a, b >∈ R. ;87XOP<=6_ b = a (4 ] I | σ ∀x1∃x2F2(x1, x2). ! 3.22 L ( I1 G 3.20, σ  L  I1 : -> σ  I1 S K2` β: ∀x1∀x2((∃x3F2(f 2 3 (x1, x3), x2) ∧ ∃x4F2(f 2 3 (x2, x4), x1)) → F2(x1, x2)) ?I1 | σ β ⇔ :/ m1 ∈ N , I1 | σ(x1/m1) ∀x2((∃x3F2(f 2 3 (x1, x3), x2) ∧ ∃x4F2(f 2 3 (x2, x4), x1)) → F2(x1, x2)). ⇔ :/ m1 ∈ N , m2 ∈ N , I1 | σ(x1/m1)(x2/m2) (∃x3F2(f 2 3 (x1, x3), x2)∧∃x4F2 (f 2 3 (x2, x4), x1)) → F2 (x1, x2). ⇔ :/ m1, m2 ∈ N , V I1 | σ(x1/m1)(x2/m2) ∃x3F2(f 2 3 (x1, x3), x2) ∧ ∃x4F2 (f 2 3 (x2, x4), x1), . I1 | σ(x1/m1)(x2/m2) F2 (x1, x2). 6